 COURSE SUMMARY
Course Title:
Calculus
Course Code:
18MAT101
Year Taught:
2018
2019
Semester:
1
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Calculus' is a course offered at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

Scope and Objectives

To enable students to understand the meaning of differentiation and integration and apply the techniques of indefinite and definite integration

Syllabus

Unit I:

Limits and continuity: Rates of Change and Limits – Calculating Limits using Limiting Laws – The Precise definition of Limit – One-Sided Limits and Limits at Infinity – Continuity – Tangents and Derivatives. Chapter-2 (Sections 2.3-2.7)

Unit II:

Differentiation: The Derivative as a Function – Differentiation Rules – The Derivative as a Rate of Change – Derivatives of Trigonometric Functions – The Chain Rule and Parametric Equations – Implicit Differentiation -nth derivatives of the functions: eax , (ax + b)n , log(ax + b), sin(ax + b) , cos(ax + b), eaxsin(bx+ c), eaxcos(bx + c) – Problems. Chapter-3 (Sections 3.1-3.6)

Unit III:

Application of Derivatives: Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching. Chapter-4 (Sections 4.1-4.4)

Unit IV:

Integration: Estimating with Finite Sums – Sigma Notation and Limits of Finite Sums – The Definite Integral – The Fundamental Theorem of Calculus – Indefinite Integrals and the Substitution Rule – Substitution and Area between Curves. Chapter-5 (Sections 5.1-5.6)

Unit V:

Techniques of Integration: Basic Integration Formulas – Integration by Parts – Integration of Rational Functions by Partial Fractions – Trigonometric Integrals – Trigonometric Substitutions– Improper Integrals. Chapter-8 (Sections 8.1-8.4, 8.8)

Textbook

1. Calculus by Finney and Thomas, Pearson, Eleventh Edition, 11th Edition, Pearson, 2009.

References

1. M. J. Strauss, G. L. Bradley and K. J. Smith, Calculus, 3rd Edition, Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), 2007.
2. S Balachandra Rao, Differential Calculus, New Age Publications, 2005.